ESSEC - WorkingGroup on Risk

 L'Institut des Actuaires s'associe au Working Group on Risk de l'ESSEC-CREARpour sa prochaine conférence sur le thème : "Tailoring Heavy Tails for a Truncated Scenario » par Prof. Maria Isabel FRAGA ALVES, DEIO & CEAUL, University of Lisbon (Portugal).

La conférence aura lieu le mercredi 31 mai à 12h30 à l'EEE- ESSEC La Défense – Salle202.

Attention, nombre de places limité. Participer à cette conférence vous permettra d'ajouter 6 points à votre score de Perfectionnement professionnel continu (PPC).   

Short bio of the speaker: 

Maria Isabel Fraga Alves is Associate Professor at the Department of Statistics and Operations Research, Faculty of Sciences, University of Lisbon. Her research interests are in the areas of extreme value theory and statistical inference for extreme values, both under a semi-parametric and parametric setups. Isabel holds a PhD in Statistics and Computation, Probability and Statistics (Univ. Lisbon, 1992)  on “Statistical Inference in Extreme Value Models”, a Habilitation Degree of Statistics and Operations Research  (Univ. Lisbon, 2004).  Former Coordinator of Center of Statistics and Applications of University of Lisbon (2006-2009), she is an Elected Member of International Statistical Institute, Member of the Bernoulli Society for Mathematical Statistics and Probability, of the Portuguese Statistical Society and Portuguese Mathematical Society. Isabel organized several international conferences: EVT2013 - Extremes in Vimeiro Today, REV2011 - Workshop on Risk & Extreme Values in Insurance and Finance, Extremes, Risk and the Environment (Invited Session to the 56th Session of the ISI, 2007).
            

Abstract:

The Pareto tailed models are widely used for assessing the risk of rare events in several fields, as large losses in insurance, size distributions of wild forest ​fi​res, large river flows with implications to flooding in hydrology and so many others. Although these power tails reveal a very large applicability to ​fit heavy-tailed phenomena, in practice natural upper bounds can appear that truncate the probability tail, such as the Maximum Possible Loss in insurance treaties or as river flows measurements in a floods scenario; in other situations, it may also be advisable to apply an upper truncation, ensuring the existence of power moments of the distribution of interest, as to obtain reasonable estimated large loss amounts in insurance. At other instances ultimately at the largest data, deviations from a Pareto tail behaviour become apparent. Along the process of tailoring these heavy tails to truncated Pareto-type distributions, the main features of characteristics of interest in the former are somehow kept, under a light truncation scenario. Given that in practice one does not always know whether the distribution is truncated or not, we consider estimators for extreme quantiles, useful for truncated and non-truncated Pareto-type distributions. The estimator of the tail index for the truncated Pareto distribution proposed in Aban et al. (2006) is used under this truncated Pareto type setup. We also propose a truncated Pareto QQ-plot and a formal test for truncation in order to help deciding between a truncated and a non-truncated case. In this way we enlarge the possibilities of extreme value modelling using Pareto tails, o​ff​ering an alternative scenario by adding a truncation point T that is large with respect to the available data. In the mathematical modelling we hence let T→∞ at different speeds compared to the limiting fraction (k/n→0) of data used in the extreme value estimation. The method leads to quantile estimators which are especially effective in the case of rough truncation. Moreover, an estimator for extremal quantiles of the underlying non-truncated Pareto-type distribution is also proposed for situations when this is relevant.
Joint work with Jan Beirlant (KU Leuven) and Ivette Gomes (Lisbon University).
 
A l'initiative du Centre de Recherche sur le Risque - CREAR - de l'ESSEC, avec le soutien de l'Institut des Actuaires, et du bureau Banque-Finance-Assurance de la Société Française de Statistique, le WGR organise environ deux fois par mois des conférences sur le thème des risques. Réunissant professionnels, universitaires et étudiants, et coordonnées par Marie Kratz, Professeur à l'ESSEC, les conférences données par des professionnels ou des académiques sur des sujets d'actualité peuvent être en français ou en anglais. Retrouvez toutes les informations pratiques et les précédentes conférences sur le site de CREAR-ESSEC : http://crear.essec.edu/working-group-on-risk